Silicon substrate and forming method thereof

ABSTRACT

A silicon substrate has area-selectively formed porous silicon in which porosity, pore size, and pore size distribution of a porous silicon region and a shape of the porous silicon are controlled. In a silicon forming method of immersing the silicon substrate coated with a mask layer having an opening area into a solution to which forming current is applied, and anodically forming a part of the silicon substrate from the opening area of the mask layer so as to form a porous silicon area in the silicon substrate, the forming current is increased according to degree of growth of the porous silicon such that the interface current density between a growing end part of the porous silicon and silicon substrate in the anodizing process may be substantially kept at constant.

[0001] This invention relates to a silicon (Si) substrate and a methodof forming a silicon substrate. More specifically, the invention relatesto a method for depositing a mask layer on a silicon substrate, so as toselectively form at least one kind of porous silicon regions in whichporosity (P) and pore size (R) are controlled centering around a partfrom which said mask layer is partially removed, and to a method forforming a region in which an impurity is selectively doped in one ofplural kinds of said porous silicon regions, and/or relates to a siliconsubstrate having a silicon dioxide region which is formed by oxidizingsaid porous silicon region.

BACKGROUND OF THE INVENTION

[0002] Porous Silicon (hereinafter referred to as PS) is a substance inwhich infinite numbers of pores in nanometers are formed in silicon. Theporous silicon is formed by anodic oxidation (hereinafter referred to asforming) of silicon in an electrolyte solution containing hydrogenfluoride (HF) acid. As to the porous silicon of this kind, itsfundamental forming method and physical properties have been studied asa material which can be expected to be applied to various products.

[0003] Especially, as shown in FIG. 19A, in a method of whole surfaceforming in which the whole of one surface 3 of a silicon substrate 1 isanodically formed, HF acid concentration and forming current areuniformly distributed from the whole surface of the substrate. Even ifthe forming proceeds to an arbitrary thickness (d) of a PS layer, aninterface area between porous silicon 120 (FIG. 19A) and the siliconsubstrate 1 is constant at all times. Consequently, forming conditionsdo not drastically change with forming depth (d). That is, even if theforming is continued at constant forming current 121 (FIG. 19B), HF acidconcentration and PS/Si interface current density (I.D.C.) 122 (FIG.19B) can be easily kept at constant. Accordingly, this method makes itpossible to obtain porosity 131 (FIG. 19C) and pore size 132 (FIG. 19C)independent on the forming depth (d), and there have been reported anumber of studies about it as an optimum method for studying arelationship between a porous silicon forming method and physicalproperties of the porous silicon. Among these studies, [1] R. Herino, G.Bomchil, K. Barla, C. Bertrand, and J. L. Ginoux, J.Electrochem. Soc.134, 1994(1987) states details of a relationship between formingconditions and physical properties of the porous silicon to be formed inthe whole surface forming.

[0004] As to a method of depositing a mask layer on a silicon substrate,and anodizing the silicon substrate centering around an opening area ofsaid mask layer so as to selectively form the porous silicon region(hereinafter this method is referred to as selective forming), there arefollowing major documents [2] [5]: [2] P. Steiner and W. Lang, Thin SoldFilms 255, 52 (1995), [3] K. Imai and H. Unno, IEEE Trans. ElectronDevices ED31, 297 (1984), [4] V. P. Bondarenko, V. S. Varichenko, A. M.Dorofeev, N. M. Kazyuchits, V. A. Labunov, and V. F. Stel'malkh, Tech.Phys. Lett. 19, 463 (1993), [5] V. P. Bondarenko, A. M. Dorofeev, and N.M. Kazuchits, Microelectronic Engineering 28, 447 (1995) and so on. Theabove documents [2] [5] introduce a method of the forming in a conditionthat the forming current is kept at constant.

[0005] The document [4] indicates that selectively formed PS is oxidizedand employed for an optical waveguide. However, it does not give adetail explanation about factors of change in a refractive index forconfining light in the waveguide. Further, the document [5] indicatesthat an impurity can be doped into the selectively formed PS. However,it does not disclose a thought that an impurity is selectively dopedinto a specific PS region.

[0006] On the other hand, as to a known document for changing formingcurrent with time in PS forming, [6] M. Berger et al. PCT/DE96/00913discloses a method for it. Also, [7] A. Loni, L. T. Canham, M. G.Berger, R. Arens-Fischer, H. Munder, H. Luth, H. F. Arrand, and T. M.Benson, Thin Solid Film 279, 143 (1996) discloses a method for steeplychanging continuous direct current in stages, thereby forming poroussilicon in which porosity intermittently changes depending on currentvalue.

[0007] The above prior arts [6] and [7] mainly disclose that themultilayer porous silicon having high porosity (60% or more) is formedand grown into an optical waveguide itself by employing the propertythat the refractive index of the porous silicon depends on the porosity,and disclose that the porous silicon is oxidized and the silicon dioxidewhich is not densified in a porous state, is grown into an opticalwaveguide. In the documents [6] and [7], forming current is changed withtime and in stages, and kept at constant for a predetermined period.

[0008] As to documents mainly aiming at forming by pulse current, thefollowing documents are given: [8] Xiao-yuan Hou, Hong-lei Fan, Lei Xu,Fu-long Zhang, Min-quan Li, Ming-ren Yu, and Xun Wang, Appl. Phys.Lett., 68, 2323 (1996), and [9] L. V. Belyakov, D. N. Goryachev, and O.M. Sreseli, Tech. Phys. Lett. 22,97 (1996). Both of the documents [8]and [9] compare an effect of the pulse current with that of continuousdirect current in the whole surface forming of the silicon substrate.However, they disclose nothing about the selective forming.

[0009] Next, as to documents about oxidation of the porous silicon,there are following documents: [10] J. J. Yon, K. Balra, R. Herino, andG. Bomchil, J. Appl. Phys., 62, 1042 (1987), and [11] K. Balra, R.Herino, and G. Bomchil, J. Appl. Phys., 59, 439 (1986).

[0010] The above technical literatures [10] and [11] concern oxidationof porous silicon of the whole surface forming, but do not concernselectively formed porous silicon. They emphasize the importance ofporosity control because volume expansion and shrinkage caused byoxidation considerably depend on porosity. However, these documentsstate that the volume expansion caused by oxidation affects increase ofthickness of a silicon dioxide film in the whole surface forming even ifthe porosity is equal to or lower than the later-explained criticalporosity.

[0011] All of the above-mentioned prior arts [1] [11] do not disclose athought for designing porosity of the selectively formed porous siliconto be constant. The selective forming has following problems.

[0012] As shown in FIG. 17 for the later-described compared example,when the selective forming is carried out in the silicon substrate 1(FIG. 17A) on which the mask layer 3 having an opening area 7 isdeposited, an interface area 111 (FIG. 17B) between the porous silicon100 and silicon 1 changes (increases) as the forming proceeds. If theforming is carried out at constant forming current, interface currentdensity 113 (FIG. 17C) in an interface 102 between porous silicon 100and silicon 1 (FIG. 17D) relatively decreases as the forming proceeds.Accordingly, both of porosity 115 (FIG. 17D) and pore size of the poroussilicon also decrease as the forming proceeds, wherein there is aproblem that these values cannot be kept at constant. Further, in theselective forming, a lot of problems are caused by a limited conditionthat a supply route for HF in the forming solution, a supply route forforming current, and an escape route for anodic gas generated in theforming concentrate into the part 7 (FIG. 17A) from which said masklayer is removed.

[0013] In addition, various problems are caused by the volume changeafter oxidizing the porous silicon in the selective forming. Lowporosity expands the volume after oxidation, and partially brings aboutinside stress on the PS/Si interface, which reduces the reliability ofthe applied devices. However, high porosity extremely shrink the volumeafter oxidation. If the porous silicon is applied to an opticalwaveguide and so on, the volume shrinkage makes it difficult to form thewaveguide having a desirable shape. This invention makes it possible tominimize the volume expansion and shrinkage of the porous silicon afterthe oxidation by porosity control of the selectively-formed poroussilicon, and besides, allows the selective doping of an impurity by poresize control.

SUMMARY OF THE INVENTION

[0014] This invention is made in the above-described background. Firstobject of the present invention is to provide a silicon substrate havinga porous silicon region in which porosity, pore size, pore sizedistribution and PS/Si interface shape are controlled into predeterminedvalues in selective forming of the porous silicon region on one surfaceof the silicon substrate, and to provide methods for forming saidsilicon substrate. The first method is a method for directly formingporous silicon having any desired porosity, pore size and pore sizedistribution. The second method is a method for forming porous siliconhaving porosity, pore size and pore size distribution of specificvalues, and then partially oxidizing the formed porous silicon. Thepartial oxidation of the porous silicon expands the volume of thesilicon according to degree of oxidation, so that a fraction of porespaces decreases. That is, this increases the volume of solid partsconsisting of silicon column and silicon dioxide in the porous silicon,and decreases pore size. On the other hand, if the oxide film is removedby dilute HF acid, the volume of solid parts is decreased, and pore sizeis increased. Employing combination of these effects, this method formsthe porous silicon having any desired porosity, pore size and pore sizedistribution. Second object of the present invention is to provide amethod of continuously forming plural kinds of porous silicon regionseach of which has any desired porosity, pore size and pore sizedistribution. Third object of the present invention is to provide amethod of selectively doping a desired impurity into a specified regionof plural porous silicon regions, and provide a silicon substrate inwhich physical properties of the specified region are controlled. Fourthobject of the present invention is to minimize the volume change of theporous silicon before and after oxidation, thereby providing a siliconsubstrate in which a surface of the formed silicon dioxide region is inthe same plane as an original surface of the silicon substrate, andproviding a forming method of said silicon substrate.

[0015] In order to achieve the above-mentioned objects, in a siliconsubstrate in which a silicon dioxide region is selectively formed in onesurface, when depth of said silicon dioxide region is “b”, anddifference between the surface of said silicon dioxide region and onesurface of said silicon substrate is “c+d”, the value (c+d)/b isdesigned to be in a range of ±13%.

[0016] According to a silicon substrate in which a porous silicon regionis selectively formed in one surface, porosity of said porous siliconregion is designed to be from 52% to 65%.

[0017] Further, in a method of forming a silicon substrate wherein saidsilicon substrate which is clad by a mask layer having an opening areais immersed into a forming solution to which forming current is applied,and then a part of the silicon substrate is anodized from the openingarea of the mask layer so as to selectively form a porous silicon regionin the silicon substrate, the forming current is changed dependent ondegree of growth of the porous silicon such that the interface currentdensity between a growing end part of the porous silicon and siliconsubstrate in the anodic forming process may be substantially kept atconstant.

[0018] Furthermore, in a method of forming a silicon substrate, theforming current is pulse current, and applying time per unit pulseand/or repeating time thereof are changed with growth of the poroussilicon region.

[0019] Moreover, in a method of forming a silicon substrate, whereinsaid silicon substrate which is clad by a mask layer having an openingarea is immersed into a forming solution to which forming current isapplied, and then a part of the silicon substrate is anodically formedfrom the opening area of the mask layer so as to selectively form aporous silicon region in the silicon substrate, the porous siliconregion is formed, following which, an oxide film is formed on thesurface of said porous silicon region.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] FIGS. 1A-1C are views showing a forming method of a siliconsubstrate; FIG. 1A is a perspective cross sectional view, FIG. 1B is aview showing dependence of forming current 21 and interface currentdensity 22 on forming depth “r”, and FIG. 1C is a view showing thatporosity 31 and pore size 32 are designed to be substantially constantindependent on the forming depth;

[0021] FIGS. 2A-2B are views showing a forming method of a siliconsubstrate; FIG. 2A is a view showing a detailed pattern of applyingpulse current 80, FIG. 2B is a view showing a summarized pattern of thepulse current in an initial stage 81, a middle stage 82, and a closingstage 83;

[0022]FIG. 3 is a view showing that porosity and pore size arecontrolled into arbitrary values by choosing HF acid concentration andforming current density, and showing desirable combination of porosityand pore size in the case of selectively doping an impurity into poroussilicon and/or oxidizing the porous silicon;

[0023] FIGS. 4A-4C is a view showing partial oxidation of the poroussilicon; FIG. 4A shows a relationship between a reciprocal of absolutetemperature and a fraction of silicon dioxide, FIG. 4B schematicallyshows silicon column 62 and pore size 63 in the porous silicon, and FIG.4C schematically shows silicon columns 64 and oxide films 65 inpartially oxidized porous silicon;

[0024]FIG. 5 is a schematic view showing a method of forming poroussilicon region having arbitrary porosity and pore size by combination ofprocesses for partial oxidation and removal of oxide film;

[0025] FIGS. 6A-6C are views showing a method of forming a multilayerporous silicon region in which porosity and pore size have controlledvalues; FIG. 6A is a cross-sectional view, FIG. 6B shows a controllingmethod of forming current, interface current density and HF acidconcentration, and FIG. 6C schematically shows forming depth dependenceof controlled porosity and pore size in plural layers;

[0026]FIG. 7 is a view showing an example of forming a partial regioninside a core region in an optical waveguide;

[0027] FIGS. 8A-8B are views showing a relationship between porosity ofthe porous silicon and volume change after oxidizing the porous silicon;FIG. 8A shows the relationship for a wide range of porosity, and FIG. 8Bshows the relationship for a narrow range of porosity;

[0028] FIGS. 9A-9C are views showing shapes of the silicon dioxidesurface after oxidizing the selectively-formed porous silicon; FIG. 9Ais a cross-sectional view, FIG. 9B shows a whole shape of a crosssection, and FIG. 9C shows the silicon dioxide surface in detail;

[0029]FIG. 10 is an already-known view showing a relationship betweenconcentration of various metal oxides and fluorine (F) which are mixedinto the silicon dioxide, and a refractive index of mixtures;

[0030] FIGS. 11A-11B are views showing a relationship betweenconcentration of titanium dioxide mixed into the porous silicon andimpurity doping critical porosity P_(imp); FIG. 11A shows therelationship for a wide range of concentration, and FIG. 11B shows therelationship for a narrow range of concentration;

[0031] FIGS. 12A-12B schematically show a control method of themultilayer porous silicon in the case of selectively doping a highlyconcentrated impurity; FIG. 12A is a cross sectional view, and FIG. 12Bis forming depth dependence of porosity and pore size;

[0032]FIG. 13 is a view showing a relationship between porosity and poresize in the case of selectively doping a highly concentrated impurity;

[0033] FIGS. 14A-14E are cross sectional views showing a basicmanufacturing method of an optical waveguide;

[0034] FIGS. 15A-15C are views showing an example of near field pattern(N.F.P.) of light transmitted in the optical waveguide;

[0035]FIG. 16 is a view showing an example of mask opening widthdependence of spot size of the light transmitted in the opticalwaveguide;

[0036] FIGS. 17A-17D are views showing a compared example; FIG. 17A is aperspective cross sectional view, FIG. 17B is a view showing formingdepth dependence of interface area, FIG. 17C is a view showing formingdepth dependence of interface current density, and FIG. 17D is a viewschematically showing forming depth dependence of porosity;

[0037]FIG. 18 is a cross sectional view showing dimensions for adetailed analysis of a cross-sectional shape of the oxidized poroussilicon in the compared example; and

[0038] FIGS. 19A-19C are views concerning growth of the porous siliconin conventional whole surface forming; FIG. 19A is a perspective crosssectional view, FIG. 19B is a view showing forming depth independence offorming current and interface current density, and FIG. 19C is a viewshowing forming depth independence of porosity and pore size.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT OF THE PRESENTINVENTION

[0039] Hereafter, the embodiments of the present invention will beexplained with reference to the accompanying drawings.

[0040] Basic characteristics of porous silicon are determined byporosity (P), pore size (R), and pore size distribution (R). It is notedthat the porosity (P) is defined by volume percentages of pores throughthe whole volume of the porous silicon, the pore size (R) is defined asdiameter of pores, and the pore size distribution (R) is defined as thedistribution of pore size.

[0041] As to the porous silicon, its porosity (P), pore size (R), andpore size distribution (R) depend on doping characteristics of a siliconsubstrate to be used, HF (hydrofluoric) acid concentration, andinterface current density between the porous silicon and a siliconinterface. In the case of a highly doped p-type silicon substrate, theporosity, pore size, and pore size distribution are changed as shown inFIG. 3. In FIG. 3, ▪ show peak values in the pore size distribution, andand  show values of full width at half maximum of the distribution. Asto comments in rounded rectangles, upper lines show HF acidconcentration, and lower lines show the interface current densitybetween porous silicon and silicon.

[0042] The Applicant composed FIG. 3 in a whole surface formingcondition about the relationship between forming conditions and physicalproperties of the porous silicon, based on each of data reported in theabove-mentioned study [1]. The figure points out important fourproperties of the porous silicon. First, the porosity and the pore sizeincrease as the interface current density increases. Second, theporosity and the pore size decrease as the HF acid concentrationincreases. Third, increasing the HF acid concentration induces anarrowing of the pore size distribution. Particularly, using HF acid ina highly concentration induces an extreme narrowing of the pore sizedistribution, and the porosity becomes uniform. Fourth, the figureindicates that porous silicon having any desired porosity, pore size,and pore size distribution can be achieved by choosing the formingconditions of the HF acid concentration and interface current density.

[0043] Further, FIG. 3 indicates that, when the formed porous silicon isoxidized, it is required that the porosity be designed to be criticalporosity (about 55%) as a desirable condition.

[0044] The present invention provides a method for forming poroussilicon which satisfies the above-mentioned condition in the selectiveforming.

[0045] Considering usual concentration of the HF acid used in theconventional method, the present invention employs the HF acidconcentration of up to about 50% that is the highest concentration tosupply for industrial purposes, and besides, when further highlyconcentrated HF acid is required, it may employ the highestconcentration. The interface current density is up to dozens ofamperes/cm2.

[0046] Using the highly concentrated HF acid greatly enhances interfacesmoothness between the porous silicon and silicon compared to the caseof lowly concentrated HF acid.

[0047] When the porous silicon of the silicon substrate in the presentinvention is oxidized, and then, employed for a single-mode opticalwaveguide, it is desired that the porous silicon have mask opening width“w” of 20μm or less. Although there is no especially limited conditionsabout the smallest value of the mask opening width “w”, a width withgood reproducibility is industrially desired in usual microstructureprocesses. If the mask opening width “w” becomes larger than 20μm, itbecomes difficult to design the condition for single-mode transmission.However, there is no upper limit of the mask opening width “w” inmulti-mode optical waveguides.

[0048] Similarly, in the case of using the porous silicon as asingle-mode optical waveguide, it is desired that forming depth “r” ofthe porous silicon be 100 μm or less. Within this range, the poroussilicon can satisfy a function as the optical waveguide. If the formingdepth “r” exceeds the above range, a region to be processed becomeslarger than required. However, in the case of applying the poroussilicon to a multi-mode optical waveguide, forming depth is not limited.

[0049] The above-mentioned limitations of the mask opening width “w”,and forming depth “r” are determined based on a necessary and sufficientcondition as the optical waveguide when the porous silicon is used forthe optical waveguide. When the porous silicon is applied to otherfields, these values can be flexibly determined.

First Embodiment for Controlling Porosity and Pore Size

[0050] Hereafter, first embodiment of the present invention is explainedreferring to the drawings. FIG. 1A is a perspective cross sectionalview, FIG. 1B is a view showing a method of controlling forming currentso as to correspond to forming depth “r”, and FIG. 1C is a view showinga dependence on forming depth “r” of the porosity and pore size of theformed porous silicon. In the present invention, it is desired that thesilicon substrate 1 be a p-type silicon substrate having holeconcentration of 1×10¹⁸ cm3 or more, that is, specific resistance of 0.1m or less. However, the substrate which supplies uniform chargedelectrons and holes to the interface between the porous silicon andsilicon in the PS forming, basically satisfies the conditions of thepresent invention. In FIG. 1A, a mask layer 5 consisting of siliconnitride (SiNx) and so on, is deposited on one surface 3 of the siliconsubstrate 1, and on said mask layer 5, an opening area 7 which extendsto a certain direction and has opening width “w” is formed byphoto-etching and the like. Anodic forming of the silicon substrate inan electrolyte solution including HF acid uniformly forms a poroussilicon region 11 having forming depth “r” (radius in porous region)starting from an end part of the opening area 7.

[0051] In the above-mentioned selective forming, at a certain point inthe process of growing the porous silicon, an area of an interface 19between the porous silicon 11 and silicon 1 per unit length is given byan equation below:

L=πr+w  (1)

[0052] When current per unit length which concentrates into the maskopening width “w” is denoted by I, interface current density J betweenthe porous silicon 11 and silicon 1 is determined by an equation below:

J=I/L=/(πr+w)  (2)

[0053] If the forming is carried out at constant current I, theinterface current density J decreases in accordance with the aboveequation (2) (explained in a later-described compared example, refer toFIG. 17C). While the interface current density J is relatively high atan initial stage of the forming in which the forming depth “r” is smallrelative to the mask opening width “w”, the interface current density Jextremely decreases when “r” becomes large relative to the mask openingwidth “w” (i.e., r>w) as the porous silicon grows.

[0054] In order to fix the interface current density J at constant, itis needed to satisfy the equation:

I=J*L=J*(πr+w)  (3)

[0055] by increasing the forming current I in proportion to theinterface area between the porous silicon 11 and silicon 1. That is, itis required to control the forming current as a function of formingdepth “r” so as to maintain I=f(r). An example of controlling theforming current is schematically shown by solid line 21 in FIG. 1B.Dotted line 22 denoting a constant value controlled as shown in FIG. 1Bindicates the interface current density controlled to constant value.

[0056] As indicated in the above equation (3), in order to keep theinterface current density J (22) between the porous silicon 11 andsilicon 1 at constant, it is desired that forming current I (21) becontrolled so as to increase in proportion to the increase of theinterface area. Thus, when the interface current density 22 is kept atconstant, porosity 31 and pore size 32 of the porous silicon 11 takes onconstant values independent on the forming depth “r” as shown in FIG.1C.

[0057] Controlling forming current as described above carries a largeamount of concentrated current into the mask opening area 7 with theincrease of the forming depth “r” as shown in equation (3). Further,said forming current generates a large amount of anode gas from theinterface between the porous silicon 11 and silicon 1. The escape routeof said gas is limited to the opening area 7 having the width “w”.Therefore, if forming current is controlled simply in a continuousdirect current, there occurs a problem that the mask layer 5 isdestroyed by pressure of a large amount of the generated gas. Thisproduces cracks and delaminating of the mask. The cracks anddelaminating of the mask layer 5 prevent the achievement of the objectto selectively form a porous silicon region only in the desired part.Besides, the supply route for an electrolyte solution containing HF isalso limited to the narrow opening area 7 with the width “w”, whichproduces a problem of making it difficult to maintain the constant HFacid concentration in the forming solution consumed by the PS forming.

[0058] In order to avoid these problems, as shown in FIG. 2A, theforming is carried out by employing pulse current 80 having effectivepeak current value Ip, and effective peak duration time tp, andrepeating period T. In this case, the effective peak current value iscontrolled so as to satisfy equations (2) and (3), or the condition ofcurrent value 21 in FIG. 1B. The pulse current carries out the forming,which can maintain high interface current density. On the other hand,the gas generated by the application of the pulse current can be escapedfrom the mask opening area 7 having the width “w” even during pulsestopping. Further, the electrolyte solution is supplied to the forminginterface with the escape of the gas. Thus, the pulse current value Ip,duration time tp per unit pulse, and repeating period T are controlledsuch that average current value per unit time Ip*tp/T can be controlledto within a range for preventing the cracks and delaminating of the masklayer 5. The current value during pulse stopping (T tp) is notnecessarily required to be zero, but cathode current may be carried.

[0059]FIG. 2B schematically shows a conceptional relationship betweenpulse current value, time span for applying the current, time span forstopping the current in an initial stage 81, a middle stage 82, and aclosing stage 83 of the forming. It is also possible to carry out acomplex control which applies continuous direct current for smallcurrent density, and applies pulse current for large current density.

[0060] The above-described method allows the forming in the condition ofthe highly concentrated HF acid and high interface current density.Thereby, combining of lowly concentrated HF acid and low interfacecurrent density, this enables to directly form the porous silicon havingcontrolled porosity and pore size in a wide area.

Second Embodiment

[0061] Second embodiment for designing any desired porosity and poresize is explained hereafter. In this embodiment, an initial processforms a porous silicon having a specified porosity and pore size, andthen a following process transforms the porous silicon into a poroussilicon having any desired porosity and pore size.

[0062]FIG. 4A shows a relationship between fraction of the oxidizedporous silicon and oxidation temperature in a treatment that the poroussilicon is oxidized in dry oxygen atmosphere for long enough time (1hour or more). The treatment at 300° C. (1000/T=1.74) grows silicondioxide of nearly monomolecular layer on a surface of densified siliconcolumn 62 inside the porous silicon. In this treatment, fraction of theoxidized porous silicon is about 15%. The treatment at 350° C.(1000/T=1.6) oxidizes about 30% of silicon, and grows silicon dioxide ofnearly bimolecular layer. Further, the treatment at 800 oxidizes almostall amount of the silicon. In the treatment at the middle temperaturetherebetween, fraction of silicon dioxide depends on a reciprocal ofabsolute temperature as shown in FIG. 4A. Growth of monomolecular layersilicon dioxide reduces pore size by 0.5 nm (nanometers) because ofvolume expansion associated with oxidation. That is, pore size ofsilicon dioxide can be reduced in response to the degree of oxidation.

[0063]FIG. 4B is a schematic view showing a microstructure of poroussilicon region. The porous silicon has infinite numbers of siliconcolumn 62 cross-sectional size of which is in nanometers, and pores 63size of which is almost same as the silicon column 62, which arealternately arranged. Size of the pores is denoted by R1 i 63. When theporous silicon is partially oxidized in dry oxygen atmosphere, thesurface of silicon column 62 is oxidized for growing an oxide film 65 asshown in FIG. 4C. In the silicon column 62, fraction of the oxide film65 and silicon remainder 64 depends on oxidation temperature as shown inFIG. 4A. The oxidation expands the silicon volume by two times comparedto the volume before the oxidation. Consequently, sum volume ofremainder silicon column 64 and oxide film 65 also expands, whichresultantly reduces pore size R1 o 66 of the partially oxidized poroussilicon. Thus, the partial oxidation of the porous silicon enables tocontrol the pore size to be smaller than an original size.

[0064] On the other hand, the silicon dioxide part is removed from thepartially oxidized porous silicon by etching in a dilute HF solution.Therefore, remainder silicon 64 becomes narrower than silicon column 62.As a result, effective pore size R2 i 67 becomes larger than originalpore size R1 i 63, and porosity also increases. The increase rate ofpore size and porosity can be controlled by the fraction of the partialoxidation.

[0065]FIG. 5 schematically shows a process of combining partialoxidation and removal of the oxide film. The process starts with formingporous silicon designated as α. Then, the porous silicon is partiallyoxidized for transforming to state . After that, the oxide film isremoved for transforming to state. Similarly, this process isappropriately repeated from states to state. Thereby, the porous siliconhaving any desired porosity and pore size can be formed.

[0066] In the above process, the porous silicon having specified smallporosity and pore size is formed, and then, the porous silicon istransformed into the porous silicon having any desired porosity and poresize by the combination of said partial oxidation process and removalprocess of the oxide film.

Multilayer Forming

[0067]FIG. 6 shows an embodiment for forming the porous silicon havingplural layers each of which has different characteristic. As shown inFIG. 6A, a first porous silicon region 13 having specified porosity andpore size, and a second porous silicon region 15 enclosing said firstporous silicon region 13 are formed. FIG. 6B shows a relationshipbetween HF acid concentration 41 and 43 (dashed lines), current values23 and 25 (solid lines) and interface current density 24 and 26 (dottedlines) in the forming of the porous silicon regions. The first poroussilicon region 13 is formed by the first HF acid concentration 41, andfirst interface current density 24. After that, the second poroussilicon region 15 is formed by the second HF acid concentration 43 andsecond interface current density 26. In this case, the second HF acidconcentration 43 is designed to be higher than the first HF acidconcentration 41, and the second current density 26 is designed to behigher than the first current density 24 in correspondence with adifference between the first and second HF acid concentrations. Choosingthese forming parameters substantially equalizes porosity 33 and 35(solid lines) of the first and second porous silicon (P1=P2), anddesigns pore size 34 (dotted line) of the first porous silicon region 13to be larger than pore size 36 of the second porous silicon region 15.

[0068] Choosing the forming conditions as mentioned above allows each ofporous silicon regions to have any desired porosity and pore size.

[0069] As an application of the above method, it is certainly possibleto form another partial region 12 inside the first porous silicon region13 as shown in FIG. 7.

Impurity Doping

[0070] As shown in FIG. 6C, the pore size 34 of the first porous siliconregion 13 which is formed by the method explained in FIG. 6, is designedto be larger than the pore size 36 of the second porous silicon region15. Immersing the silicon substrate 1 on which plural porous siliconregions are formed, into an organic metal compound solution includingmetal elements, achieves selective doping of a metal organic compoundinto the porous silicon region 13 having pores of larger size.

[0071] Said metal organic compound may contain metal elements such as:aluminum (Al), boron (B), barium (Ba), bismuth (Bi), calcium (Ca),cadmium (Cd), cerium (Ce), cesium (Cs), dysprosium (Dy), erbium (Er),europium (Eu), gadolinium (Gd), germanium (Ge), hafnium (Hf), holmium(Ho), indium (In), lanthanum (La), lutetium (Lu), magnesium (Mg),niobium (Nb), neodymium (Nd), phosphorus (P), promethium (Pm),praseodymium (Pr), rubidium (Rb), antimony (Sb), samarium (Sm), tin(Sn), strontium (Sr), tantalum (Ta), terbium (Tb), titanium (Ti),thallium (Tl), thulium (Tm), yttrium (Y), ytterbium (Yb), tungsten (W),zinc (Zn), zirconium (Zr).

[0072] Among the above-mentioned metal elements, for example, boron (B)has a property for decreasing a refractive index in the silicon dioxide.Further, zirconium (Zr) and titanium (Ti) increase a refractive index.Furthermore, rare earth elements such as erbium (Er) which are opticallyactive impurities in silicon dioxide, have a property of lightamplification and the like.

[0073] In the case of applying the porous silicon to the opticalwaveguide as described later, as to the elements for decreasing therefractive index, it is possible to dope them into both of the firstporous silicon region 13 and second porous silicon region 15 shown inFIG. 6. On the other hand, as to the elements for increasing therefractive index, it is desired to selectively dope them only into thefirst porous silicon region 13. As to optically active rare earthelements, they can be doped into the first porous silicon region 13,besides, if it is necessary, as shown in FIG. 7, it is also possible toselectively dope them only into the partial region 12 in the region 13.As to selective doping of plural elements having different propertiesinto different regions, metal organic compound molecules consisting ofelements having a property for decreasing the refractive index aredecreased in size; metal organic compound molecules consisting ofelements having a property for increasing the refractive index areincreased in size; and metal organic compound molecules consisting ofelements such as optically active rare earth are further increased insize. Thereby, the selective doping is achieved in response to the poresize of each of porous silicon regions. In this process, changing sizesof metal organic compound molecules to be doped is allowed by prior artsas an object for designing metal organic compound molecules.Consequently, choosing combination between pore size and molecular sizemakes it possible to selectively dope the elements having variousproperties.

Problems Associated with Oxidation and Solution Thereof

[0074] The explanation is nextly given to how to control characteristicsof the porous silicon in the case of oxidizing the above-formed poroussilicon for growing the silicon dioxide in wet oxygen ambient, watervapor and so on.

[0075] Oxidation expands silicon volume. Porosity should be controlledsuch that pores of the porous silicon may be compensatively filled bythe volume expansion due to the oxidation. This transforms the poroussilicon into the closely-packed silicon dioxide without changing anoriginal shape of the porous silicon region. Required conditions are asfollows:

[0076] (a) Volume of 1 mol of silicon VSi is:

VSi=ZSi/Si  (5)

[0077]  here, Z represents molar equivalent, and represents specificgravity.

[0078] (b) When this silicon is transformed into porous silicon havingconstant porosity P, silicon existing in the above volume is (1 P) mol.

[0079] (c) When the above silicon of (1 P) mol is oxidized and melted,the volume of the silicon dioxide becomes:

VSiO2=(1P)*ZSiO2/SiO2  (6)

[0080] (d) Critical porosity Po is defined as porosity which equalizesthe above volumes (5) and (6), which means making no change in thevolume after oxidation, the following equations are given:

Po=1(SiO2/Si)*(ZSi/ZSiO2)=1 A  (7)

A=(SiO2/Si)*(ZSi/ZSiO2)  (8)

[0081] here, represents specific gravity, Z represents molar equivalent,and Si and SiO2 denote silicon and silicon dioxide respectively.Substituting the following well-known physical property value into aboveequations (7) and (8),

[0082] ZSi=28.0855 g/mol

[0083] ZSiO2=60.0843 g/mol

[0084] Si=2.3291 g/cm3

[0085] SiO2=2.24 g/cm3

[0086] gives critical porosity Po=55.0%.

[0087] Moreover, if the porosity is changed by P from Po, the volumechange VSiO2 is given by the equation below:

VSiO2=P*(ZSiO2/ZSi)/(Si/SiO2)=P/A=2.224 P  (9)

[0088] That is, when the porosity changes by 1%, the volume change isVsio2=2.224%.

[0089]FIG. 8 shows a relationship concerning the volume change betweenthe above-mentioned porous silicon porosity P and silicon dioxide SiO2.FIG. 8A is a view showing it for a wide range of porosity from 48% to62%. FIG. 8B is a view showing it for a narrow range of porosity from53% to 57%. As shown in figures, when porosity is controlled to thecritical porosity Po, the volume change after oxidizing the poroussilicon becomes zero. Thus, the volume occupied by the porous silicon isentirely replaced by the volume of dense silicon dioxide. When theporosity is larger than Po (P>0), the volume shrinks. When the porosityis smaller than Po (P<0), the volume expands. The volume changecoefficient is P/A as mentioned above. This theory holds in either ofthe selective forming and whole surface forming.

[0090] Hereafter, a problem of volume change associated with theselective forming which concerns a main object of the present inventionwill be explained. Here, the study is given to a cross-sectional shapeof the oxidized porous silicon which is formed in the embodiment shownin FIGS. 1A to 1C. As an example of parameters, w=6 μm, and r=27 μm aregiven. FIG. 9A shows coordinates in the cross-sectional shape of theporous silicon including silicon dioxide 53 which is formed by oxidizingand melting. A y-coordinate is defined in the silicon substrate 1,starting from an intersection point of the center of mask opening width“w” and the original surface of the silicon substrate 1. A x-coordinateis defined along with the substrate surface 3, starting from the centerof mask opening width “w”.

[0091] As to the surface shape of the silicon dioxide which is obtainedby oxidizing the selectively formed porous silicon region, each of valueis calculated as follows. The shape of an interface 50 between thesilicon dioxide and silicon is represented by the following equations:

y={r2(x w/2)2}½ [x]w/2  (10)

y=r [x]w/2  (11)

[0092] In these equations, x and y represent positions on thecoordinates in FIG. 9A, and r, w and [x] respectively represent a radiusin the porous silicon forming, mask opening width and absolute value ofx.

[0093] Next, it is assumed that, as to the volume change such asexpansion and shrinkage due to oxidation, influence of the volume changeis avoided by raising and lowering the surface (free surface) of thesilicon dioxide. Thereby, a surface position y on an arbitraryx-coordinate is given by the equations below:

y={r2(x w/2)2}½*P/A [x]w/2  (12)

y=r*P/A [x]w/2  (13)

[0094] A result of the above calculation is shown in FIGS. 9B and 9C.FIG. 9B shows the shape of the interface between the silicon dioxide andsilicon, and FIG. 9C shows the shape of the silicon dioxide surface 51in detail. In FIG. 9C, numerical values on curved lines represent P inpercentage.

[0095] It is clear from these figures that, especially in the conditionof P=0% (P=Po), the silicon dioxide surface is in the same plane withthe original surface 3 of the silicon substrate. FIG. 9C shows anexample of the interface shape according to the volume expansion in thecondition that P is negative, and shows a detailed example of theinterface shape according to the volume shrinkage in the condition thatP is positive.

[0096] Further, y-coordinate value in the center of mask opening width“w” is shown in table 1. TABLE 1 ΔP y-position ΔP y-position (0/0) (μm)(0/0) (μm) 0.00 0.000 0.00 0.000 −1.00 0.598 1.00 −0.598 −2.00 1.1962.00 −1.196 −3.00 1.794 3.00 −1.794 −4.00 2.392 4.00 −2.392 −5.00 2.9905.00 −2.990 −6.00 3.588 6.00 −3.588

[0097] As shown in Table 1, in the case that P is within a range of ±6%,the maximum displacement of the y-position is as small as about 3.6 m.In the case that P is within a range of ±3%, the maximum displacement isabout 1.8 μm. These values are much smaller than those of thelater-explained compared example are.

[0098] As described above, in the case of the oxidation of the poroussilicon, it is desired that the porosity be in the range from 52% to62%. This is because, the lower limit 52% is smaller than the abovecritical porosity Po by 3%, and the volume expansion in the oxidation ofthe porous silicon is reduced by one-half or more compared to the poroussilicon formed by the conventional method described later in thecompared example. Also, the upper limit 65% is the impurity dopingcritical porosity in the case of doping titanium dioxide of about 5 mol% into silicon dioxide.

[0099] If the porosity is controlled as mentioned above, the poroussilicon can be designed so as not to expand nor shrink its volume afterthe oxidation relative to the volume of the porous silicon before theoxidation. Accordingly, as shown in FIG. 9A, the surface 51 of thesilicon dioxide 53 can be designed to be in the same plane as theoriginal surface 3 of the silicon substrate 1.

In the Case of Doping a Highly Concentrated Impurity

[0100]FIGS. 8 and 9 show a relationship between porosity and volumechange in oxidation of the porous silicon.

[0101] Hereafter, the explanation is given to an embodiment forminimizing the volume change of the porous silicon into which animpurity is doped after oxidization. In an optical waveguide shown inthe later-described FIG. 14, a refractive index is increased by dopingtitanium into first porous silicon region 55. On the other hand, noelement is doped into second porous silicon region 57 that is used as acladding. If the silicon dioxide is used as an optical waveguide, thoughthe refractive index difference between the core and cladding is mostlydetermined by conditions for designing an optical waveguide, thedifference of the refractive index as large as about 2% may be employedto a waveguide having large difference of the refractive indexes. FIG.10 shows a well-known relationship between the impurity concentrationand refractive index in the case of adding various impurities into thesilicon dioxide (quartz glass), which is normalized by the refractiveindex of the silicon dioxide. In order to give 2% of the difference ofthe refractive index, impurity concentration to add is required to beabout 5% in ZrO2, 6% in TiO2, or further higher in Al203 and GeO2.

[0102] As described above, in the case of oxidizing the porous siliconin which a highly-concentrated impurity was doped, the volume expansionassociated with the oxides of the added impurity elements should beconsidered for forming the porous silicon.

[0103] Theory in this case is similar to the previously described caseshown in FIG. 8:

[0104] (a) Volume of 1 mol of silicon VSi is:

VSi=ZSi/Si  (5)

[0105] (b) When this silicon is transformed into porous silicon havingconstant porosity P, silicon existing in the above volume is (1 P) mol.

[0106] (c) When the above silicon of (1 P) mol is oxidized and melted,the volume of the silicon dioxide becomes:

VSiO2=(1 P)*ZSiO2/SiO2  (6)

[0107] (d) Relative to (1 P) mol of silicon dioxide, the volume of x molof the added oxidized impurity is:

Vimp=x/(1 P)*Zimp/imp  (14)

[0108] (e) In order to equalize the sum volume of (6) and (14) to thevolume of (5), the equation below should be satisfied:

ZSi/Si=(1 P)ZSiO2/SiO2+{x/(1 P)*Zimp/imp}  (15)

[0109] That is, if impurity doping critical porosity Pimp is therequired condition for making no change in the volume after oxidizingthe impurity-doped porous silicon, the equation below is given:

P _(imp)=1{A/2+(A2/4x*B)}½  (16)

[0110] In the above equation,

A=(ZSi/ZSiO2)*(SiO2/Si)  (8)

B=(Z _(imp) /ZSiO2)*(SiO2/imp)

[0111] In these equations, x represents a mole ratio of the addedoxidized impurity element to the silicon dioxide. If titanium dioxide(TiO2) as an example of an impurity to add, and rutile-type crystaldensity are employed considering specific gravity , the followingequations are given:

imp=TiO2=4.23 g/cm3,

Z _(imp) =ZTiO2=79.8788 g/mol

[0112] In the above equation (16), impurity doping critical porosityPimp is shown in FIG. 11 as a function of a mole ratio x. In the figure,the horizontal axis shows mole ratios of titanium dioxide (TiO2) tosilicon dioxide (SiO2), and the vertical axis shows critical porosityP_(imp) in the case of doping the impurity having a correspondingconcentration.

[0113]FIG. 11A shows a range from 0% to 5% as x. FIG. 11B shows a rangefrom 0% to 2% in detail. As shown in the figure, if 2 mol of titaniumdioxide (TiO2) is added, the impurity doping critical porosity Pimpincreases to 58% or more. Further, if 5 mol of titanium dioxide (TiO2)is added, the impurity doping critical porosity P_(imp) increases to 65%or more.

[0114] The above-mentioned value becomes considerably bigger than thecritical porosity Po=55% shown in FIG. 8. When the highly-concentratedimpurity is doped, an effect caused by the volume of the doped impurityto the porous silicon volume after oxidization should be previouslyconsidered. A method for forming the porous silicon in this case isshown in FIG. 12. In FIGS. 12A and 12B, it is desired that porosity 37of first porous silicon region 19 be designed to be the impurity dopingcritical porosity P_(imp), and the porosity of second silicon region bethe critical porosity Po.

[0115] If titanium of any desired high concentration is doped into theporous silicon which is formed considering the above-mentionedconditions, following which, the porous silicon is oxidized, the twokinds of surfaces of silicon dioxide can be maintained to be in the sameplane as the original surface of the silicon substrate.

[0116]FIG. 13 shows a fundamental thought of this embodiment of thepresent invention. In order to form the first porous silicon regionwhich grows into an impurity doping silicon dioxide region, porosityshould be previously designed to be large. That is, in order to form thesilicon dioxide in which the impurity is doped, it is required to formthe porous silicon having critical porosity Poimp corresponding to thedoping concentration. Further, in order to form the silicon dioxide inwhich no impurity is doped, it is required to form the porous siliconhaving critical porosity Po.

Process to Form Optical Waveguide

[0117] Referring to FIG. 14, a fundamental concept about a formingmethod for forming an optical waveguide which is an application exampleof the present invention. As shown in FIG. 14A, the forming methodstarts with a process of depositing a thin-film mask layer 5 on onesurface 3 of the silicon substrate 1, and forming an opening area 7having any desired width “w” by photo-etching. Then, the first poroussilicon region 13 is formed on the substrate 1 as the anode in a firstforming condition, following which, the second porous silicon region 15is formed in a second forming condition (FIG. 14B).

[0118] Especially, when no impurity is doped into the second poroussilicon region 15, it is desired that the porosity of the second poroussilicon region 15 be designed to be the above-mentioned criticalporosity Po to minimize the volume change after oxidation. Further, ifan impurity is doped into the first porous silicon region 13, it isdesired that the porosity of first porous silicon region 13 be designedto be the above-mentioned impurity doping critical porosity Poimp inconsideration of an effect of the doped impurity to the volume afteroxidation. Furthermore, regarding the pore size R, it is desired thatpore size R13 of the first porous silicon region 13 be designed to belarger than pore size R15 of the second porous silicon region 15.Besides, in connection with molecular size R_(imp) of an impurity whichwill be doped into a next procedure, designing a relationship of R13R_(imp) R15 enables the selective doping of the impurity in the nextprocedure.

[0119] The substrate on which multi layer porous silicon is formed, isimmersed into a titanium organic compound solution, after that, thecompound solution depositing on the substrate surface is removed. Thisprocess dopes impurity molecules into pores of first porous siliconregion 13, and the first porous silicon region 13 grows into a region 17in which the impurity is doped (FIG. 14C). Since the pore size of thesecond porous silicon region 15 is smaller than molecular size of theimpurity, the impurity cannot be entered into the pores of the secondsilicon region 15.

[0120] Then, the substrate 1 is oxidized for about an hour at forexample 1150 C. in wet oxygen atmosphere. After that, the mask layer 5is removed by etching (FIG. 14). This oxidation process transforms thefirst porous silicon region 13 in which titanium was doped, into a coreregion 55 having an increased refractive index. Also, since a secondporous silicon region 15 is silicon dioxide (SiO2) into which noimpurity was doped, this process transforms it into a cladding 57 havinga lower refractive index. Thus, this completes an optical waveguide.Then, it is possible to form an upper cladding layer 59 when required(FIG. 9E).

[0121] In an optical waveguide structure shown in FIG. 14D is formed ina condition of w=0.75 to 6 μm, and r=27 μm, laser light of wavelength1.55 μm was introduced from one end of the optical waveguide, and nearfield pattern (NFP) is measured.

[0122]FIG. 15 shows an example of the NFP of the optical waveguide whichis formed in a condition of w=6 μm. FIG. 15A shows a distribution oflight intensity of horizontal direction to the substrate, and FIG. 15Bshows a light intensity distribution in vertical direction. FIG. 15Cshows intensity contour. The NFP is symmetric in horizontal direction tothe substrate surface. On the other hand, asymmetry of the NFP invertical direction to the substrate surface is due to an abrupt changeof the refractive index in the optical waveguide which has no uppercladding layer as shown in the structure of FIG. 14D. As shown in thefigure, the intensity of the introduced light is transmitted by singlemode, and centered at a single peak.

[0123]FIG. 16 shows an example of dependence of the introduced lightspot size on mask opening width “w”. As shown in the figure, when themask opening width “w” is between 4 and 6 μm, the introduced light istransmitted by single mode. When the mask opening width “w” is less than4 μm, the width of NFP increases as the mask opening width “w”decreases. If the mask opening width “w” is 3 μm or less, the NFP showsplural peaks, which indicates that the transmitted light is multimode.In this embodiment, when the mask opening width “w” becomes small, thetransmitted light becomes multimode. This is due to the decrease of theeffect for increasing the refractive index in the core region since thequantity of doped titanium decreases as the opening width “w” decreases.[Compared example]

[0124] As is the case with FIG. 1A, mask layer 5 of a thin siliconnitride film is deposited on one surface 3 of the silicon substrate 1having a specific resistance of 0.01 m in which highly-concentrated B isdoped, and the mask opening area 7 with the width w is formed on themask layer (FIG. 17A). After that, a porous silicon region is formed atconstant forming current. As shown in FIG. 17B, an area of the interface102 between porous silicon 100 and silicon increases per unit length asfollows:

L=πr+w

[0125] Since the forming current is constant, as shown in FIG. 17C,interface current density in the interface between the porous siliconand silicon decreases as the porous silicon grows. The figure shows anexample in the case of w=6 μm, normalizing an initial interface currentdensity as 1. Thus, since the interface current density decreases withthe forming depth, porosity 115 of the porous silicon region 100decreases with the forming depth as shown in FIG. 17C. In the initialstage of the forming, interface current density of an interface 102between the porous silicon 100 and silicon 1 is considerably high, butthe current density greatly decreases as the porous silicon grows. Then,in the closing stage of the forming, the interface current densitybecomes extremely lower than the initial value. In an example shown inthe figure, when the forming depth “r” is 30 μm, the interface currentdensity decreases to 6% relative to the initial value. As a result, asshown in FIG. 17D, while the porosity is high at the initial stage ofthe forming, the porosity is low at the closing stage.

[0126] The porous silicon is oxidized and melted for an about 1 hour at1150 C. in wet oxygen atmosphere. A typical example of the cross sectionof such silicon dioxide is shown in FIG. 18. Volume shrinkage isobserved at a center part 152 of the silicon dioxide region 150, andvolume expansion of oxide is obviously observed at parts 154 adjacent tothe interface with the silicon. This result shows that, while the oxidearound the interface is influenced by compressive stress, the siliconadjacent to the interface is partially influenced by tensile stress. Ifa test sample formed in the above-mentioned manner is placed at a roomtemperature for about one month, a microscopic observation shows a crosssection in which chips are frequently generated in an interface part 154between volume-expanded silicon dioxide and TABLE 2 w Length: μm Ratioof Length (μm) a b c d a/b (a − w)/b c/b: % d/b: % (c + d)/b % 0.7552.74 25.14 3.63 3.42 2.10 2.068 14.44 13.62 28.07 0.75 52.40 24.66 3.563.01 2.13 2.095 14.44 12.22 26.67 6.00 61.44 26.91 3.74 3.74 2.28 2.06013.90 13.90 27.81 6.00 59.29 26.64 3.93 3.21 2.23 2.000 14.75 12.0626.81 6.00 59.52 26.81 3.95 3.33 2.22 1.996 14.74 12.43 27.18 6.00 59.9526.35 4.03 3.55 2.28 2.047 15.29 13.49 28.78 average 57.56 26.08 3.813.38 2.20 2.045 14.59 12.96 27.55

[0127] silicon by microstructure chipping. That is, the interfacebetween the porous silicon and silicon partially contains high stress.

[0128] On the other hand, length a, b, c and d defined by arrows in FIG.18 is shown in table 2 as a result measured in a scanning electronmicroscopy picture for plural test samples.

[0129] Table 2 shows examples when the mask opening width “w” is 6.0 μmand 0.75 μm. Value of horizontal width “a” distributes in a considerablewide range (about 52-6 μm). On the other hand, value a/b slightlyexceeds 2. In further detail, value (a—w)/b approximates 2.0. Even ifexperimental errors are considered, this result indicates that theforming of the porous silicon is isotopic as explained above.

[0130] On the other hand, value (c+d) which is sum value of volumeexpansion and shrinkage is about 7 μm. The average value of (c+d)/d isas large as about 27%, which indicates that volume expansion andshrinkage coexist with each other, and each of them is considerablylarge.

[0131] Compared with the above-described value, the embodiment shown inFIG. 9 shows the expansion or shrinkage value 3.6 m in P=±6%, and theforming depth 13% which is ½ of that of the present embodiment. Thisshows importance and effectiveness of the porosity control and volumechange control after oxidation by the method in accordance with thepresent invention.

[0132] The present invention is not limited to the above-describedembodiment, but includes varied or modified embodiments from the above.

[0133] As described above, a silicon substrate in a condition that depthof a silicon dioxide region which is selectively formed on one surface,is “b”, and a difference between said one surface of the siliconsubstrate and the surface of the silicon dioxide region is “c+d”, thevalue (c+d)/b is designed to be within a range of ±6%, is extremelyadvantageous to mounting of optical elements such as optical fiber andthe like as an optical module substrate, compared with a conventionaloptical module which is formed by thick-film depositing and etching. Inthis silicon substrate, it is possible to relieve large amount ofpartial stress contained in an interface between the silicon dioxide andsilicon, thereby allowing to manufacture a device having stablereliability, in which the silicon dioxide and the silicon are in contactwith each other, especially an optical waveguide.

[0134] In a silicon substrate, porous silicon which is selectivelyformed on one surface of the silicon substrate, has porosity designed tobe from 52 to 62%; therefore, if an optical waveguide is formed byutilizing said porous silicon, an upper surface of a core and a claddingaround said core is designed to be in the same plane as an originalsurface of the silicon substrate. The silicon substrate in which thecore surface of the optical waveguide is in the same plane as theoriginal surface of the silicon substrate, is extremely advantageous, asan optical module substrate, to mounting of optical elements such asoptical fiber and the like compared with a conventional optical modulewhich is formed by thick-film depositing and etching.

[0135] In a method for forming a silicon substrate, forming current isincreased in accordance with growing degree of porous silicon so as tomaintain interface current density between a growing end part of theporous silicon and the silicon substrate to be constant in a process ofanodic forming, thereby making it possible to form the porous siliconhaving porosity and pore size which are selectively controlled insilicon crystal. Also, this method enables to form multilayer poroussilicon having same porosity and different sizes, and to selectivelydope an impurity into one of said plural porous silicon layers. Besides,porous silicon having plural layers each of which has previouslydesigned porosity and pore size can be formed. This method further makesit possible to form porous silicon in which pore size and porosity isdesigned according to the impurity to dope and impurity concentration,and to selectively dope the impurity into one of said porous silicon,and allows to develop a method of introducing critical porosity forminimizing volume change of the porous silicon after oxidation. Due tothe above-mentioned method, an optical waveguide is formed such that anupper surface of a core and a cladding around the core can be in thesame plane as the original surface of the silicon substrate. The siliconsubstrate in which the core surface of the optical waveguide is in thesame plane as the original surface of the silicon substrate isadvantageous to mounting of optical elements such as optical fiber andthe like compared with a conventional optical module which is formed bythick-film depositing and etching. Moreover, using the method of thepresent invention further makes it possible to relieve large amount ofpartial stress contained in an interface between the silicon dioxide andsilicon, thereby allowing to manufacture a device having stablereliability, in which the silicon dioxide and the silicon are in contactwith each other, especially an optical waveguide.

[0136] Further, in a method for forming a silicon substrate, a poroussilicon region is formed in the silicon substrate by an anodizingprocess, following which, oxide film is formed on a surface of theporous silicon region, so that this method enables to form the poroussilicon region in which pore size further decreases than the pore sizeimmediately after the anodic oxidation. Also, the porous silicon havingincreased porosity and increased pore size can be formed by etching theoxide film formed on the surface of the porous silicon region. Theprocess of the partial oxidation and removal of the oxide film canprovide the second method for forming the second porous silicon havingany desired porosity, pore size and pore size distribution.

What is claimed is:
 1. A silicon substrate in which a silicon dioxideregion is selectively formed in a buried state in one surface, wherein,if depth of said silicon dioxide region is “b”, a distance to a lowestpoint of the surface of the silicon dioxide region is “c”, and adistance to a highest point of the surface of the silicon dioxide regionis “d”, relative to said one surface of the silicon substrate, value(c+d)/b is 13% and less.
 2. The silicon substrate in which a silicondioxide region is selectively formed in one surface according to claim 1, wherein said silicon dioxide region comprises a first silicon dioxideregion which has a predetermined refractive index, and a second silicondioxide region which lies inside the silicon substrate so as to enclosesaid first silicon dioxide region, and has a smaller refractive indexthan that of the first silicon dioxide region.
 3. The silicon substratein which a silicon dioxide region is selectively formed in one surfaceaccording to claim 2 , wherein said silicon dioxide region has the firstsilicon dioxide region, and the second silicon dioxide region which liesinside the silicon substrate so as to enclose said first region, andwherein said first silicon dioxide region contains elements forincreasing a refractive index of silicon dioxide, and concentration ofsaid elements is higher than those of the second silicon dioxide region.4. The silicon substrate according to claim 3 , wherein the element forincreasing the refractive index of the silicon dioxide is at least oneelement selected from a group consisting of zirconium (Zr), titanium(Ti), aluminum (Al), germanium (Ge) and phosphorus (P).
 5. The siliconsubstrate in which the silicon dioxide region is selectively formed inone surface according to claim 2 , wherein said silicon dioxide regioncontains transition metal elements in the first region having apredetermined refractive index, and comprises the second silicon dioxideregion which lies in the silicon substrate so as to enclose said firstsilicon dioxide region, and has the smaller refractive index than thatof the first silicon dioxide region.
 6. A silicon substrate in which aporous silicon region is selectively formed in one surface, wherein saidporous silicon region has porosity in a range from 52% to 65%.
 7. Thesilicon substrate in which the silicon dioxide region is selectivelyformed in one surface according to claim 6 , comprising plural poroussilicon regions, wherein pore size of the first porous silicon region islarger than pore size of the second porous silicon region.